Far from the edge, \(\mathbf {A}_{2\omega } (\mathbf {r})\)  represents the outgoing cylindrical wave. Its parameters can be found by analyzing the asymptotic of
\(\mathbf {A}_{2\omega } (\mathbf {r})\)  at large \(R = \sqrt{x^2 + z^2}\) . The asymptotic expansion of the Hankel function at large arguments has the form
\(\mathrm {H}_0^{(1)}(\xi ) \approx \sqrt{2/(\pi \xi }) \exp (\mathrm {i}\xi - \mathrm {i}\pi /4)\) . Then, in the far field zone, i.e., at \(R \gg 2\pi /k_{2\omega }\) , and in the dipole approximation [1]}, which suggests \(k_{2\omega } l \ll 2\pi \) , where \(l\)  is the width of the stripe where the edge current flows,
the field is given by
\(\mathbf {A}_{2\omega } (\mathbf {r}) = \frac{\mathrm {i}\sqrt{2\pi }}{c \sqrt{k_{2\omega } R}} \exp \left[ \mathrm {i}\left( k_{2\omega } R - \frac{\pi }{4}\right) \right] \mathbf {J}_{2\omega } \:,\) 
